Multiscale Analysis of Laminated Composite Beams and Plates for Computational Design of High-Performance Engineering Materials (SCALE-LAMINATE) - CNS2022-135900

The SCALE-LAMINATE project has developed a reliable, physically sound, and computationally efficient multiscale strategy for the analysis of reinforced composite laminates across three observation scales: macroscopic, mesoscopic, and microscopic.

The multiscale framework operates as a weak coupling between the macroscopic and mesoscopic scales, employing computational homogenization theory within a tailor-made FE² scheme. The third scale (microscale) is incorporated throughout the framework using the rule of mixtures.

One of the key features of the approach is its rigorous interpretation of energetic equivalence between scales, linking bodies of different dimensionality—namely, the macroscopic shell and the mesoscopic filament. The dimensional reduction applied at the macroscale (from a 3D solid to a 2D shell) and at the mesoscale (from a 3D solid to a 1D filament) significantly reduces computational cost and, consequently, enhances performance. Results obtained with this multiscale framework demonstrate speedups of up to three orders of magnitude in demanding numerical experiments when compared to full 3D analyses.

The framework developed in this project has been evaluated in terms of the accuracy of the resulting stress fields against equivalent reference 3D computations. The results show high accuracy, establishing the method as a valuable and cost-effective tool for simulating such materials. Furthermore, the framework is general with respect to the nonlinear constitutive behavior adopted at the lower scales.

As in standard FE² schemes, the key idea is that the mesoscopic constitutive response naturally emerges from the solution of a boundary value problem (BVP) defined at the representative volume element (RVE) level. This contrasts with alternative approaches, such as the Refined Zig-Zag Theory, where mesoscopic behavior is prescribed through ad hoc functions that lack generality in representing complex mechanical behavior.

The proposed technology inherently supports the concept of materials-by-design, as modifications to material properties at lower scales directly influence macrostructural behavior through the consistent interscale coupling provided by the multiscale framework.

 

Publications

1.      P. Wierna, D. Yago, Lloberas-Valls O., A.E. Huespe and J. Oliver. On the Efficient and Accurate Non-linear Computational Modeling of Multilayered Bending Plates. State of the Art and a Novel Proposal: The  Multiscale 2D+ Approach. Arch Computat Methods Eng 31, 2451–2506, 2024.

2.      J. Triclot and O. Lloberas-Valls. Proof of concept implementation in ABAQUS of the 2D+ multiscale approach for non-linear analysis of multilayered bending flat shells. To be submitted to “Finite Elements in Analysis and Design”.

Conference Presentations

1.      ECCOMAS 2024

2.      CMN 2024

3.      ESMC 2025

4.      CM3P 2025

5.      WCCM 2026

6.      CMN 2026